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Goldbach's Conjecture states that every even integer greater than 2 can be expressed as the sum of two prime numbers. This conjecture has been tested up to 4 quintillion (or 4*10^18) and has held true. However, it remains unproven, even though many people throughout the history of mathematics have attempted to prove it.

Goldbach

Christian Goldbach

Goldbach Partitions

A Goldbach partition is the expression of an even number as the sum of two primes. The following are Goldbach partitions of the first 20 numbers:

  • 4=2+2
  • 6=3+3
  • 8=5+3
  • 10=7+3
  • 12=5+7
  • 14=3+11
  • 16=5+11
  • 18=7+11
  • 20=13+7

Certain numbers have many Goldbach partitions.

Goldbach Conjecture (Proven)

I think we are in the final shown. Because as stated in the article, with the two set [p; p_{1}; p_{2}.....] = 2N and [(2a+1); (2b+1); (2c+1);.....] = 2B. We have. (2a+1) + (2b+1) = 2B (2A+1) + (2C+1) = 2b_{1}

If we apply the decomposition of each pair.

[(2a+1) - 2] + [(2b+1) +2] = 2B

Being (2a+1) the minor of the odd not prime, then.

[(2a+1) -2] = p

Turn: [(2b+1) + 2] \neq (2c+1) then [(2b+1) + 2]< (2c+1) with the which.

[(2b+1) + 2] = p_{n}

And so on. Therefore all: 2N = [p + (2a+1); p + p_{n}; p_{n} (2a+1); (2a+1) + (2n+1)]

Published in: http://www.hrpub.org/journals/jour_info.php?id= 24 Vol 3 (3) 2015

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